Question

Condense each expression to a single logarithm
36 ln x + 6 ln y

Answer 1

`\bf \begin{array}{llll} \textit{logarithm of factors} \\\\ \log_a(xy)\implies \log_a(x)+\log_a(y) \end{array} ~\hfill \begin{array}{llll} \textit{Logarithm of exponentials} \\\\ \log_a\left( x^b \right)\implies b\cdot \log_a(x) \end{array} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ 36ln(x)+6ln(y)\implies ln\left( x^(36) \right)+ln\left( y^6 \right)\implies ln\left( x^(36)\cdot y^6 \right) \\\\\\ ln(x^(6\cdot 6)\cdot y^6)\implies ln[(x^6)^6y^6]\implies ln\left[ (x^6y)^6 \right]`

Answer 2

36x+6y

Explanation: